In most cases, for fixed monomial ordering \(\prec \) , only the bases
for the degree reducing interpolation space
\(\mathcal {P}\subset \Pi ^2\) (see [1]}) are pursued for
Lagrange interpolation (REF ). Let \(\lbrace p_1, \ldots , p_\mu \rbrace \) 
be a basis for \(\mathcal {P}\)  satisfying \(p_1 \prec p_2\prec \cdots \prec p_\mu \) . If
\(p_j(\xi ^{(i)})=\delta _{ij},\quad 1\le i \le j \le \mu ,\) 
